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What is Tridiagonal Matrix?

Indata structure a tridiagonal matrix is a matrix in which there are no non-zero elements in the main diagonal, the first diagonal which is exactly below the main diagonal and the first diagonal which is exactly above the main diagonal

This is an example of the tridiagonal matrix in which the main diagonal which consist of numbers 1,4,3,3 are non-zero elements. Furthermore the diagonal above the main diagonal also does not contain any null components; the diagonal below the main diagonal also shows the same features.

The Tridiagonal matrix is also referred to as Thomas algorithm. It is a simplified version of the Gaussian elimination theorem and thus helps us solve tridiagonal system of equations.

In data structure, using the help of transformation a Hermitian matrix can be resolved and can be transformed into a tridiagonal matrix. So many algorithms using the transformation are converted into tridiagonal matrix.

The tridigonal matrix can be of many advantages to the computer language. It is stored easily in comparison to the general matrix. It requires a special storage scheme for them to be easily stored in the memory.

For example

A package called the LAPAK stores an unsymmetrical array of n order into a tridiagonal matrix in which one length contains n elements defined in the array and the other two has n-1 elements in them

Apart from the programming world, the tridiagonal matrix shows many advantages.

Many linear algebraic algorithms require less effort when they use the tridiagonal matrix.